Note that it is possible to go on to an (n,n+1)(n,n+1)-category, or (n+1)(n+1)-poset. You can either consider than the nn-cells are ordered, or else consider that there are irreversible (n+1)(n+1)-cells which are indistinguishable. (Reversible indistinguishable (n+1)(n+1)-cells are all identities and so might as well not exist.)